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Question

The graph which depicts the result of Rutherford's gold foil experiment with α-particle is

θ: Scattering angle

Y: Number of scattered α- particles detected

(Plots are schematic and not to scale)


A
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B
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C
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D
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Solution

The correct option is B

Step 1: Given data:

θ: Scattering angle

Y: Number of scattered α- particles detected

Step 2: Formula Used:

According to Rutherford's observations from the gold foil experiment-

Nθ=Ksin4θ4

Where, K is constant,

Nθ is no. of alpha particles scattered through an angle θ

Step 3: Computing the graph between Yandθ:

From the scattering formula,

Nθ=Ksin4θ4

Here, Y: number of scattered α- particles detected

Yα1sinθ44

When,

θ=2πθ4=π2

Since 0to2π function sin4θ4increases so 1sin4θ4decreases

So, At θ0,sin0=0,1sin4θ/4=

Thus the graph will decrease exponentially.

Note that this figure which depicts the result of Rutherford's gold foil experiment with α-particles will be

Therefore the α-particle isYα1sinθ24.

Hence,option B is the correct answer.


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